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Qiaochu Yuan
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Here is a puzzle Scott Garrabrant posted on Facebook that some of you might enjoy:

"Pi Day Puzzle: Using the number 3 repeated 14 times, and unlimited uses of the operations addition, subtraction, multiplication, division, exponentiation, and factorial, how well can you approximate pi? (Factorial is only defined on the natural numbers.)

Spoiler: I expect most of my mathematician friends are not yet very interested in this puzzle, since it looks like a programming puzzle. Here is a hint to make it more interesting. You can get arbitrarily good approximations. How do you do it?"

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Post on the problem of logical uncertainty: how do we deal with uncertainty about mathematical facts such as the digits of pi, or the truth of the Riemann hypothesis? 

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Ramanujan stuff.

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